Numerical methods for the extended Fisher-Kolmogorov (EFK) equation

Danumjaya, Palla ; Pani, Amiya Kumar (2006) Numerical methods for the extended Fisher-Kolmogorov (EFK) equation International Journal of Numerical Analysis and Modeling, 3 (2). pp. 186-210. ISSN 1705-5105

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In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, some a priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and regularity results for the weak solutions are derived. Using C1-conforming finite element method, optimal error estimates are established for the semidiscrete case. Finally, fully discrete schemes like backward Euler, two step backward difference and Crank-Nicolson methods are proposed, related optimal error estimates are derived and some computational experiments are discussed.

Item Type:Article
Source:Copyright of this article belongs to Global Science Press.
Keywords:Extended Fisher-Kolmogorov (EFK) Equation; Lyapunov Functional; Weak Solution; Existence; Uniqueness and Regularity Results; Finite Element Method; Semidiscrete Method; Backward Euler; Two Step Backward Difference and Crank-Nicolson Schemes; Optimal Estimates
ID Code:81956
Deposited On:09 Feb 2012 04:46
Last Modified:18 May 2016 23:19

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